Greek culture in the context of "Classical Greece"

Greece, officially the Hellenic Republic, is a country in Southeast Europe. Located on the southern tip of the Balkan peninsula, it shares land borders with Albania to the northwest, North Macedonia and Bulgaria to the north, and Turkey to the east. The Aegean Sea lies to the east of the mainland, the Ionian Sea to the west, and the Sea of Crete and the Mediterranean Sea to the south. Greece has the longest coastline on the Mediterranean basin, spanning thousands of islands and nine traditional geographic regions. It has a population of over 10 million. Athens is the nation's capital and largest city, followed by Thessaloniki, Patras and Heraclion.

Greece is considered the cradle of Western civilisation and the birthplace of democracy, Western philosophy, Western literature, historiography, political science, major scientific and mathematical principles, theatre, and the Olympic Games. The Ancient Greeks were organised into independent city-states, or poleis (singular polis), that spanned the Mediterranean and Black seas. Philip II of Macedon united most of present-day Greece in the fourth century BC, with his son Alexander the Great conquering much of the known ancient world from the Near East to northwestern India. The subsequent Hellenistic period saw the height of Greek culture and influence in antiquity. Greece was annexed by Rome in the second century BC and became an integral part of the Roman Empire and its continuation, the Byzantine Empire, where Greek culture and language were dominant. The Greek Orthodox Church, which emerged in the first century AD, helped shape modern Greek identity and transmitted Greek traditions to the wider Orthodox world.

Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the shores of the ancient Mediterranean, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of deductive reasoning in proofs is an important difference between Greek mathematics and those of preceding civilizations.

The early history of Greek mathematics is obscure, and traditional narratives of mathematical theorems found before the fifth century BC are regarded as later inventions. It is now generally accepted that treatises of deductive mathematics written in Greek began circulating around the mid-fifth century BC, but the earliest complete work on the subject is Euclid's Elements, written during the Hellenistic period. The works of renown mathematicians Archimedes and Apollonius, as well as of the astronomer Hipparchus, also belong to this period. In the Imperial Roman era, Ptolemy used trigonometry to determine the positions of stars in the sky, while Nicomachus and other ancient philosophers revived ancient number theory and harmonics. During late antiquity, Pappus of Alexandria wrote his Collection, summarizing the work of his predecessors, while Diophantus' Arithmetica dealt with the solution of arithmetic problems by way of pre-modern algebra. Later authors such as Theon of Alexandria, his daughter Hypatia, and Eutocius of Ascalon wrote commentaries on the authors making up the ancient Greek mathematical corpus.

In classical antiquity, the Hellenistic period covers the time in Greek, Eastern Mediterranean, and West Asian (or Middle Eastern) history following Classical Greece, between the death of Alexander the Great in 323 BC and the death of Cleopatra VII in 30 BC, in which these regions were under the influence of Greek leadership, culture, and language. The Hellenistic period was followed by the ascendancy of the Roman Empire, the Battle of Actium in 31 BC, and the Roman conquest of Ptolemaic Egypt the following year, which eliminated the last major Hellenistic kingdom. Its name stems from the Ancient Greek word Hellas (Ἑλλάς, Hellás), which was gradually recognized as the name for Greece, from which the modern historiographical term Hellenistic was derived. The term "Hellenistic" is to be distinguished from "Hellenic" in that the latter refers to Greece itself, while the former encompasses all the ancient territories of the period that had come under significant Greek influence, particularly the Hellenized Ancient Near East, after the conquests of Alexander the Great.

After the Macedonian conquest of the Achaemenid Empire in 330 BC and its disintegration shortly thereafter in the Partition of Babylon and subsequent Wars of the Diadochi, Hellenistic kingdoms were established throughout West Asia (Seleucid Empire, Kingdom of Pergamon), Northeast Africa (Ptolemaic Kingdom) and South Asia (Greco-Bactrian Kingdom, Indo-Greek Kingdom). This resulted in an influx of Greek colonists and the export of Greek culture and language to these new realms, a breadth spanning as far as modern-day India. These new Greek kingdoms were also influenced by regional indigenous cultures, adopting local practices which were deemed beneficial, necessary, or convenient. Hellenistic culture thus represents a fusion of the ancient Greek world with that of the Western Asian, Northeastern African, and Southwestern Asian worlds. The consequence of this mixture gave rise to a common Attic-based Greek dialect, known as Koine Greek, which became the lingua franca throughout the ancient world.

Hellenization or Hellenification is the adoption of Greek culture, religion, language, and identity by non-Greeks. In the ancient period, colonization often led to the Hellenization of indigenous people. In the Hellenistic period, many of the territories which were conquered by Alexander the Great were Hellenized.